Question

The points $(a,0),(0,b)$ and $(1,1)$ are collinear. Then the value of $\frac{1}{a}+\frac{1}{b}$ is

Answer 1

Let $A=(a,0),B=(0,b)$ and $C=(1,1)$ and $B$ divides the line segment $AC$ in the ratio of $k:1$.
Then, by section formula,
$(\frac{k+a}{k+1},\frac{k}{k+1})=(0,b)\Rightarrow k=-a$

Now, $\frac{k}{k+1}=b$
$\Rightarrow \frac{-a}{1-a}=b\Rightarrow \frac{a-1}{a}=\frac{1}{b}\therefore \frac{1}{a}+\frac{1}{b}=1$